The ComRes poll for The Independent on Sunday and Sunday Mirror newspapers showed that support for Scotland going it alone has risen sharply in recent months.
Some 39 per cent of adults in England, Wales and Northern Ireland thought Scotland should become an independent state -- up six points since May -- while 38 per cent disagree.
Scottish First Minister Alex Salmond's Scottish National Party (SNP), which advocates independence, wants to put the matter to a referendum towards the end of the five-year term his party won in May.
A spokesman for the Scotland Office, the British government ministry dealing with Scottish affairs, said Salmond's Edinburgh government had "yet to put any detail on its plans for independence to the people of Scotland".
"We will continue to demand they do so, while at the same time making the strong and positive case for (Scotland) remaining part of the United Kingdom."
SNP campaigns director Angus Robertson said the poll showed there was significant support in Scotland and England "for our nations having a new relationship of equality as two independent countries, sharing a head of state and working together as partners in Europe".
Meanwhile, the opposition Labour Party are ahead in the polls, on 39 per cent, with Prime Minister David Cameron's Conservatives on 37 per cent, Deputy Prime Minister Nick Clegg's Liberal Democrats on 10 per cent and other parties on 14 per cent, the ComRes poll revealed.
Some 30 per cent said they trusted Cameron and his finance minister George Osborne to make the right decisions about the economy, while 49 per cent disagreed.
For Labour's top team, the respective figures were 18 percent and 55 per cent. While Some 34 per cent thought Cameron was turning out to be a good premier, with 47 per cent disagreeing.
ComRes surveyed 2,004 British adults online on Wednesday and Thursday.